The manually operable dispensing pump described and claimed in the above-identified copending application dispenses fluent products in a relatively non-pulsating discharge. In some applications, such as for example when pumping viscous products, there tends to be a slight dribbling of product from the outlet passageway upon termination of pumping. The pump includes a storage compartment containing an accumulator piston which opens and closes the outlet passageway in cooperation with a check valve which admits fluent product into a pressurizing compartment feeding the storage compartment but does not allow the product to return to the container during the pressure stroke of the accuator of the pump. The pressure of the fluent product in the storage compartment acts on the accumulator piston to open the outlet passageway. Upon termination of pumping, the pressure of a spring acting on the accumulator piston causes the accumulator piston to close the outlet passageway. However, since the check valve, when closed, prevents product from returning to the container, there may be enough pressure in the storage compartment to prevent the outlet passageway from being completely closed by the accumulator piston. In this case, fluent product tends to dribble adversely out the partially closed outlet passageway when pumping ceases.